Notes on Yang-Mills--Higgs monopoles and dyons on R^D, and Chern-Simons--Higgs solitons on \R^{D-2}: Dimensional reduction of Chern-Pontryagin densities

TL;DR

This paper reviews the construction of higher-dimensional monopoles, dyons, and Chern-Simons solitons derived from Yang-Mills and Higgs fields, emphasizing dimensional reduction of Chern-Pontryagin densities across various dimensions.

Contribution

It systematically extends monopole and dyon solutions to higher dimensions and introduces new Chern-Simons densities via dimensional reduction techniques.

Findings

Constructed monopoles and dyons in 8 and higher dimensions.

Derived new Chern-Simons densities applicable in all dimensions.

Established topological bounds relating to Yang-Mills-Higgs systems.

Abstract

We review work on construction of Monopoles in higher dimensions. These are solutions to a particular class of models descending from Yang--Mills systems on even dimensional bulk, with Spheres as codimensions. The topological lower bounds on the Yang-Mills action translate to Bogomol'nyi lower bounds on the residual Yang-Mills-Higgs systems. Mostly, consideration is restricted to 8 dimensional bulk systems, but extension to the arbitrary case follows systematically. After presenting the monopoles, the corresponding dyons are also constructed. Finally, new Chern-Simons densities expressed in terms of Yang-Mills and Higgs fields are presented. These are defined in all dimensions, including in even dimensional spacetimes. They are constructed by subjecting the dimensionally reduced Chern-Pontryagin densites to further descent by two steps.